It is statistically diverse, but like most other places, each ethnic group lives in a bubble separate from the other, mostly. The density of NYC forces deep interaction between communities -- much deeper than simply judging diversity based on the different restaurants you see or the languages you might hear at the mall everyone goes to. Here's a good article about the kind of thing that's common in NYC and nowhere else: http://www.nytimes.com/2010/05/05/nyregion/05jackson.html